Is Da Vinci’s ‘Salvator Mundi’ Worth $450 Million or $454,680?

“Salvator Mundi,” the painting widely attributed to Leonardo da Vinci, sold at Christie’s auction house in New York this weekfor more than $450 million. If we were to regard a work of art as an investment, has the Leonardo generated a good return since the master painted it?

Figuring that out takes some guesstimation. After all, the painting sold for only £45 (about $125 at the time) in 1958.

Leonardo died in 1519. King Francis I of France is said to have bought the “Mona Lisa” from Leonardo or his heir, Francesco Melzi, around that time for 4,000 gold ducats.

Examples of ducats from the late 15th and early 16th century displayed on theAmerican Numismatic Society’s websiteweigh approximately 3.5 grams apiece. A troy ounce of gold contains 31.1 grams. So 4,000 gold ducats would weigh approximately 14,000 grams, or 450.1 ounces of gold. At Wednesday’s price for gold in New York of $1277.60 per ounce, that would be a bit over $575,000.

What long-term rate of return would have brought that estimated price of about $575,000 up to this week’s sale price of $450,312,500? Assuming the original amount was invested on Nov. 15, 1519 without interruption at a continuously compounding rate, an average return of slightly under 1.35% annually would have yielded this week’s sum.

That might seem surprisingly low, but over a 498-year period, even a paltry rate of return will multiply your money hundreds of times. (By “your money,” we mean your money and that of your descendants, down to something like your great-great-great-great-great-great-great-great-great-great-great-grandchildren.)

In the long run, however, the market value of fine art has tended to outperform cash, bonds and gold — but to underperform equities. Most of the return on art is psychic, not financial, measured in units of pride or pleasure.

No wonder what finance professors Elroy Dimson and Christophe Spaenjers call art an “emotional asset.” They have estimated that from 1900 through 2012, fine art produced a 2.4% average annual returnafter inflation, compared with 0.9% for cash, 1.1% for gold, 1.5% for bonds and 5.2% for stocks. (They used British financial assets, but the results are fairly similar in other markets.)

So a 1.35% return since 1519 is mediocre but not terrible. Between 1900 and 2016, after inflation, U.S. stocks returned 6.4% averaged annually, French stocks 3.3% and Italian stocks 2%, according to the Credit Suisse Global Investment Returns Yearbook by Prof. Dimson and his colleagues Paul Marsh and Mike Staunton.

That’s not the only way to reckon the return on a work of art, of course. Another method yields a much lower value in today’s terms.

A large altarpiece, says Prof. Nelson, would bring a higher price than a small portrait like “Salvator Mundi.” However, by 1500 Leonardo was “much more famous” than in 1483, says Prof. Nelson, so for speculative purposes we could assign “Salvator Mundi” the same price of 250 florins.

In their book, Prof. Nelson and his co-author, economist Richard Zeckhauser of the John F. Kennedy School of Government at Harvard University, compared art prices in Renaissance Florence to the pay of unskilled construction workers at the time.

Those wages, Prof. Nelson says in an email, “remained extremely stable between 1350 and 1527.” He estimates that 250 florins would have bought 12 years of labor by an unskilled construction worker in Florence around the time Leonardo painted “Salvator Mundi.”

Prof. Nelson says he saw “Salvator Mundi” on exhibit in London before it was restored to its present state. “If I had all the money of a Bill Gates,” he jokes, “my top bid would have been closer to [$454,680] than $450 million.”

The difference between $454,680 and $450,312,500 is huge. But a Leonardo is more than an object and more than a conventional investment. Almost nobody would frame anAppleorFacebookstock certificate, hang it on a wall and show it off to visitors. Being able to say “And here is my Leonardo,” on the other hand, has to be one of the highest psychic returns any investor could ever have.